Tightness conjecture for the rooted $K_{3,3}$ minor bound

The preceding theorem gives a bound on rooted $K_{3,3}$ minors; denote this bound by the quantity appearing in Theorem. Tightness conjecture. The bound in Theorem is tight. This conjecture asserts that the bound cannot be improved and is presented as a possible starting point for determining forbidden minor characterizations related to reducibility. The source does not provide evidence resolving its status.